Suppose that two investments have the same three payoffs, but the probability associated with each payoff differs, as illustrated in the table below: Payoff $300 $250 $200 Probabilities for Investment A 0.10 0.80 0.10 Find the expected return and standard deviation of each investment. (Round your answers to two decimal places.) For investment A, the expected value is $ and the standard deviation is $ For investment B, the expected value is $☐ and the standard deviation is $ Jill has the utility function U = 51, where I denotes the payoff. Which investment will she choose? Jill will choose investment Ken has the utility function U = 5√1. Which investment will he choose? Ken will choose investment Laura has the utility function U = 5/². Which investment will she choose? Laura will choose investment Enter your answer in each of the answer boxes. Probabilities for Investment B 0.30 0.40 0.30

Suppose that two investments have the same three payoffs, but the probability associated with each payoff differs, as illustrated in the table below: Payoff $300 $250 $200 Probabilities for Investment A 0.10 0.80 0.10 Find the expected return and standard deviation of each investment. (Round your answers to two decimal places.) For investment A, the expected value is $ and the standard deviation is $ For investment B, the expected value is $☐ and the standard deviation is $ Jill has the utility function U = 51, where I denotes the payoff. Which investment will she choose? Jill will choose investment Ken has the utility function U = 5√1. Which investment will he choose? Ken will choose investment Laura has the utility function U = 5/². Which investment will she choose? Laura will choose investment Enter your answer in each of the answer boxes. Probabilities for Investment B 0.30 0.40 0.30

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter17: Making Decisions With Uncertainty

Section: Chapter Questions

Problem 7MC

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Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages not decimals (.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. Invest $1,000 Invest $2,000 Invest $3,000 Expected Value Percent Increase Standard Deviation 1150 S 28 % $ 8 % $ Expected Return N/A Doubled Tripled : #
Given a choice between two investments with the same expected payoff: a. Most people will choose the one with the lower standard deviation b. Most people will opt for the one with the higher standard deviation c. Most people will be indifferent since the expected payoffs are the same d. Most people will calculate the variance to assess the relative risks of the two choices
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Q1) An expected utility maximiser owns a car worth £60000£60000 and has a bank account with £20000£20000. The money in the bank is safe, but there is a 50%50% probability that the car will be stolen. The utility of wealth for the agent is u(y)=ln(y)u(y)=ln⁡(y) and they have no other assets. Q2) Consider the setup from Question 1. A risk-neutral insurance company is willing to insure the car at the premium of π=£2/3π=£2/3 for every one pound of coverage. Q3) Consider the setup from Questions 1 and 2. How much profits, in expectation, does the insurance company earn on insuring the individual?
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